Accuracy Analysis of Lunar Lander Terminal Guidance Algorithm

Abstract

This article studies a proposed analytical algorithm of the terminal guidance for the lunar lander. The analytical solution, which forms the basis of the algorithm, was obtained for a constant acceleration trajectory and thrust vector orientation programs that are essentially linear with time. The main feature of the proposed algorithm is a completely analytical solution to provide the lander terminal guidance to the desired spot in 3D space when landing on the atmosphereless body with no numerical procedures. To reach 6 terminal conditions (components of position and velocity vectors at the final time) are used 6 guidance law parameters, namely time-to-go, desired value of braking deceleration, initial values of pitch and yaw angles and rates of their change. In accordance with the principle of flexible trajectories, this algorithm assumes the implementation of a regularly updated control program that ensures reaching terminal conditions from the current state that corresponds to the control program update time. The guidance law parameters, which ensure that terminal conditions are reached, are generated as a function of the current phase coordinates of a lander. The article examines an accuracy and reliability of the proposed analytical algorithm that provides the terminal guidance of the lander in 3D space through mathematical modeling of the lander guidance from the circumlunar pre-landing orbit to the desired spot near the lunar surface. A desired terminal position of the lunar lander is specified by the selenographic latitude, longitude and altitude above the lunar surface. The impact of variations in orbital parameters on the terminal guidance accuracy has been studied. By varying the five initial orbit parameters (obliquity, ascending node longitude, argument of periapsis, periapsis height, apoapsis height) when the terminal spot is fixed the statistic characteristics of the terminal guidance algorithm error according to the terminal position and velocity have been estimated.

Keywords

• lunar pinpoint landing
• terminal guidance
• lander guidance and control
• guidance algorithm accuracy analysis